The number of daily accidents in an industrial plant have a Poisson distribution with unknown parameter . Based on the previous data, the prior density of follows an exponential distribution with rate parameter 1. That is, the prior density is () = e ^ ( ), 0 < < . Suppose we observe a total of 83 accidents over the next 10 days. (a) Compute the posterior mean of . (b) Compute the value of the maximum likelihood estimator of . (c) Compare the values from the posterior mean estimator and the maximum likelihood estimator.